1. ## Sample Mean

I'm new to this site. I am a bit lost on this problem, could I request assistance? Thanks

A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more that that on average, the corporation may lose money, and if it dispenses less, the customers may complain.
BIG Corporation would like to estimate the mean amount of coffee, μ, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate μ. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.42ounces, what is the minimum sample size needed in order for BIG to be 90%confident that its estimate is within 0.08ounces of μ?

2. Originally Posted by SuZQ
I'm new to this site. I am a bit lost on this problem, could I request assistance? Thanks

A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more that that on average, the corporation may lose money, and if it dispenses less, the customers may complain.
BIG Corporation would like to estimate the mean amount of coffee, μ, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate μ. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.42ounces, what is the minimum sample size needed in order for BIG to be 90%confident that its estimate is within 0.08ounces of μ?
Use the fact that if you were constructing a confidence interval then the endpoints would be $\overline{x} \pm z_{\alpha /2} \frac{\sigma}{\sqrt{n}}$.